Topology of Bi$_2$Se$_3$ nanosheets
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914731276632064 |
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| author | Licerán, Lucas Maisel Koerhuis, Sebastiaan Vanmaekelbergh, Daniel Stoof, Henk |
| author_facet | Licerán, Lucas Maisel Koerhuis, Sebastiaan Vanmaekelbergh, Daniel Stoof, Henk |
| contents | Recently, the quantum spin-Hall edge channels of two-dimensional colloidal nanocrystals of the topological insulator Bi$_2$Se$_3$ were observed directly. Motivated by this development, we reconsider the four-band effective model which has been traditionally employed in the past to describe thin nanosheets of this material. Derived from a three-dimensional $\boldsymbol{k} \boldsymbol{\cdot} \boldsymbol{p}$ model, it physically describes the top and bottom electronic surface states at the $Γ$ point that become gapped due to the material's small thickness. However, we find that the four-band model for the surface states alone, as derived directly from the three-dimensional theory, is inadequate for the description of thin films of a few quintuple layers and even yields an incorrect topological invariant within a significant range of thicknesses. To address this limitation we propose an eight-band model which, in addition to the surface states, also incorporates the set of bulk states closest to the Fermi level. We find that the eight-band model not only captures most of the experimental observations, but also agrees with previous first-principles calculations of the $\mathbb{Z}_{2}$ invariant in thin films of varying thickness. The band inversion around the $Γ$ point, which endows the surface-like bands with topology, is shown to be enabled by the presence of the additional bulk-like states without requiring any reparametrization of the resulting effective Hamiltonian. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_02792 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topology of Bi$_2$Se$_3$ nanosheets Licerán, Lucas Maisel Koerhuis, Sebastiaan Vanmaekelbergh, Daniel Stoof, Henk Mesoscale and Nanoscale Physics Materials Science Other Condensed Matter Quantum Physics Recently, the quantum spin-Hall edge channels of two-dimensional colloidal nanocrystals of the topological insulator Bi$_2$Se$_3$ were observed directly. Motivated by this development, we reconsider the four-band effective model which has been traditionally employed in the past to describe thin nanosheets of this material. Derived from a three-dimensional $\boldsymbol{k} \boldsymbol{\cdot} \boldsymbol{p}$ model, it physically describes the top and bottom electronic surface states at the $Γ$ point that become gapped due to the material's small thickness. However, we find that the four-band model for the surface states alone, as derived directly from the three-dimensional theory, is inadequate for the description of thin films of a few quintuple layers and even yields an incorrect topological invariant within a significant range of thicknesses. To address this limitation we propose an eight-band model which, in addition to the surface states, also incorporates the set of bulk states closest to the Fermi level. We find that the eight-band model not only captures most of the experimental observations, but also agrees with previous first-principles calculations of the $\mathbb{Z}_{2}$ invariant in thin films of varying thickness. The band inversion around the $Γ$ point, which endows the surface-like bands with topology, is shown to be enabled by the presence of the additional bulk-like states without requiring any reparametrization of the resulting effective Hamiltonian. |
| title | Topology of Bi$_2$Se$_3$ nanosheets |
| topic | Mesoscale and Nanoscale Physics Materials Science Other Condensed Matter Quantum Physics |
| url | https://arxiv.org/abs/2309.02792 |